Lesson 6
Welcome
Notes:
Scatterplot Review
library(ggplot2)
data("diamonds")
ggplot(aes(x = carat, y = price), data = diamonds) +
geom_point(fill = I("#F79420"), color = I("black"), shape = 21) +
xlim(0, quantile(diamonds$carat, 0.99)) +
ylim(0, quantile(diamonds$price, 0.99))## Warning: Removed 926 rows containing missing values (geom_point).
Price and Carat Relationship
Response: Price increases with carat, but also has more variance.
Frances Gerety
Notes:
A diamonds is
The Rise of Diamonds
Notes:
ggpairs Function
Notes:
# install these if necessary
# install.packages('GGally')
# install.packages('scales')
# install.packages('memisc')
# install.packages('lattice')
# install.packages('MASS')
# install.packages('car')
# install.packages('reshape')
# install.packages('plyr')
# load the ggplot graphics package and the others
library(ggplot2)
library(GGally)
library(scales)
library(memisc)## Loading required package: lattice## Loading required package: MASS##
## Attaching package: 'memisc'## The following object is masked from 'package:scales':
##
## percent## The following objects are masked from 'package:stats':
##
## contr.sum, contr.treatment, contrasts## The following object is masked from 'package:base':
##
## as.array# sample 10,000 diamonds from the data set
set.seed(20022012)
diamond_samp <- diamonds[sample(1:length(diamonds$price), 10000), ]
ggpairs(diamond_samp)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
What are some things you notice in the ggpairs output? Response: Price is positively correlated with x, y and z.
The Demand of Diamonds
Notes:
library(gridExtra)
plot1 <- qplot(x = price, data = diamonds, binwidth = 100,
fill = I("#099D99") ) +
ggtitle('Price')
plot2 <- qplot(x = price, data = diamonds, binwidth = 0.01,
fill = I("#F79420")) +
scale_x_log10() +
ggtitle('Price (log10)')
grid.arrange(plot1, plot2, ncol = 2)
Connecting Demand and Price Distributions
Notes:
Scatterplot Transformation
qplot(x = carat, y = price, data = diamonds) +
scale_y_continuous(trans = log10_trans()) +
ggtitle("Price (log10) by Carat")
Create a new function to transform the carat variable
cuberoot_trans = function() trans_new('cuberoot', transform = function(x) x^(1/3),
inverse = function(x) x^3)Use the cuberoot_trans function
ggplot(aes(carat, price), data = diamonds) +
geom_point() +
scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
breaks = c(0.2, 0.5, 1, 2, 3)) +
scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
breaks = c(350, 1000, 5000, 10000, 15000)) +
ggtitle('Price (log10) by Cube-Root of Carat')## Warning: Removed 1683 rows containing missing values (geom_point).
Overplotting Revisited
head(sort(table(diamonds$carat), decreasing = TRUE))##
## 0.3 0.31 1.01 0.7 0.32 1
## 2604 2249 2242 1981 1840 1558head(sort(table(diamonds$price), decreasing = TRUE))##
## 605 802 625 828 776 698
## 132 127 126 125 124 121ggplot(aes(carat, price), data = diamonds) +
geom_point(alpha = 0.5, size = 0.75, position = "jitter") +
scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
breaks = c(0.2, 0.5, 1, 2, 3)) +
scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
breaks = c(350, 1000, 5000, 10000, 15000)) +
ggtitle('Price (log10) by Cube-Root of Carat')## Warning: Removed 1691 rows containing missing values (geom_point).
Other Qualitative Factors
Notes:
Price vs. Carat and Clarity
Alter the code below.
# install and load the RColorBrewer package
# install.packages('RColorBrewer')
library(RColorBrewer)
ggplot(aes(x = carat, y = price), data = diamonds) +
geom_point(aes(color = clarity), alpha = 0.5, size = 1,
position = 'jitter') +
scale_color_brewer(type = 'div',
guide = guide_legend(title = 'Clarity', reverse = T,
override.aes = list(alpha = 1, size = 2))) +
scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
breaks = c(0.2, 0.5, 1, 2, 3)) +
scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
breaks = c(350, 1000, 5000, 10000, 15000)) +
ggtitle('Price (log10) by Cube-Root of Carat and Clarity')## Warning: Removed 1693 rows containing missing values (geom_point).
Clarity and Price
Response: Yes. Condition on carat, price increases with clarity.
Price vs. Carat and Cut
Alter the code below.
ggplot(aes(x = carat, y = price, color = cut), data = diamonds) +
geom_point(alpha = 0.5, size = 1, position = 'jitter') +
scale_color_brewer(type = 'div',
guide = guide_legend(title = 'Cut', reverse = T,
override.aes = list(alpha = 1, size = 2))) +
scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
breaks = c(0.2, 0.5, 1, 2, 3)) +
scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
breaks = c(350, 1000, 5000, 10000, 15000)) +
ggtitle('Price (log10) by Cube-Root of Carat and Cut')## Warning: Removed 1696 rows containing missing values (geom_point).
Cut and Price
Response: No. Most of the cuts are ideal and the pattern is not clear.
Price vs. Carat and Color
Alter the code below.
ggplot(aes(x = carat, y = price, color = color), data = diamonds) +
geom_point(alpha = 0.5, size = 1, position = 'jitter') +
scale_color_brewer(type = 'div',
guide = guide_legend(title = "Color",
override.aes = list(alpha = 1, size = 2))) +
scale_x_continuous(trans = cuberoot_trans(), limits = c(0.2, 3),
breaks = c(0.2, 0.5, 1, 2, 3)) +
scale_y_continuous(trans = log10_trans(), limits = c(350, 15000),
breaks = c(350, 1000, 5000, 10000, 15000)) +
ggtitle('Price (log10) by Cube-Root of Carat and Color')## Warning: Removed 1688 rows containing missing values (geom_point).
Color and Price
Response: Yes. The diamonds with better color have higher prices.
Linear Models in R
Notes:
Response: log(price) ~ carat ^ (1 / 3)
Building the Linear Model
Notes:
m1 <- lm(I(log(price)) ~ I(carat^(1/3)), data = diamonds)
m2 <- update(m1, ~ . + carat)
m3 <- update(m2, ~ . + cut)
m4 <- update(m3, ~ . + color)
m5 <- update(m4, ~ . + clarity)
mtable(m1, m2, m3, m4, m5)##
## Calls:
## m1: lm(formula = I(log(price)) ~ I(carat^(1/3)), data = diamonds)
## m2: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat, data = diamonds)
## m3: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut, data = diamonds)
## m4: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut + color,
## data = diamonds)
## m5: lm(formula = I(log(price)) ~ I(carat^(1/3)) + carat + cut + color +
## clarity, data = diamonds)
##
## =========================================================================
## m1 m2 m3 m4 m5
## -------------------------------------------------------------------------
## (Intercept) 2.821*** 1.039*** 0.874*** 0.932*** 0.415***
## (0.006) (0.019) (0.019) (0.017) (0.010)
## I(carat^(1/3)) 5.558*** 8.568*** 8.703*** 8.438*** 9.144***
## (0.007) (0.032) (0.031) (0.028) (0.016)
## carat -1.137*** -1.163*** -0.992*** -1.093***
## (0.012) (0.011) (0.010) (0.006)
## cut: .L 0.224*** 0.224*** 0.120***
## (0.004) (0.004) (0.002)
## cut: .Q -0.062*** -0.062*** -0.031***
## (0.004) (0.003) (0.002)
## cut: .C 0.051*** 0.052*** 0.014***
## (0.003) (0.003) (0.002)
## cut: ^4 0.018*** 0.018*** -0.002
## (0.003) (0.002) (0.001)
## color: .L -0.373*** -0.441***
## (0.003) (0.002)
## color: .Q -0.129*** -0.093***
## (0.003) (0.002)
## color: .C 0.001 -0.013***
## (0.003) (0.002)
## color: ^4 0.029*** 0.012***
## (0.003) (0.002)
## color: ^5 -0.016*** -0.003*
## (0.003) (0.001)
## color: ^6 -0.023*** 0.001
## (0.002) (0.001)
## clarity: .L 0.907***
## (0.003)
## clarity: .Q -0.240***
## (0.003)
## clarity: .C 0.131***
## (0.003)
## clarity: ^4 -0.063***
## (0.002)
## clarity: ^5 0.026***
## (0.002)
## clarity: ^6 -0.002
## (0.002)
## clarity: ^7 0.032***
## (0.001)
## -------------------------------------------------------------------------
## R-squared 0.9 0.9 0.9 1.0 1.0
## adj. R-squared 0.9 0.9 0.9 1.0 1.0
## sigma 0.3 0.3 0.3 0.2 0.1
## F 652012.1 387489.4 138654.5 87959.5 173791.1
## p 0.0 0.0 0.0 0.0 0.0
## Log-likelihood -7962.5 -3631.3 -1837.4 4235.2 34091.3
## Deviance 4242.8 3613.4 3380.8 2699.2 892.2
## AIC 15931.0 7270.6 3690.8 -8442.5 -68140.5
## BIC 15957.7 7306.2 3762.0 -8317.9 -67953.7
## N 53940 53940 53940 53940 53940
## =========================================================================Notice how adding cut to our model does not help explain much of the variance in the price of diamonds. This fits with out exploration earlier.
Model Problems
Video Notes:
Research: (Take some time to come up with 2-4 problems for the model) (You should 10-20 min on this)
Response: The prices can change across time. The changes can vary among different carat sizes.
A Bigger, Better Data Set
Notes:
# install.packages('bitops')
# install.packages('RCurl')
# library('bitops')
# library('RCurl')
#
# diamondsurl = getBinaryURL("https://raw.github.com/solomonm/diamonds-data/master/BigDiamonds.Rda")
# load(rawConnection(diamondsurl))The code used to obtain the data is available here: https://github.com/solomonm/diamonds-data
Building a Model Using the Big Diamonds Data Set
Notes:
diamondsbig <- read.csv("diamondsbig.csv")
diamondsbig$logprice = log(diamondsbig$price)
m1 <- lm(logprice ~ I(carat^(1/3)),
data = subset(diamondsbig, price < 10000 & cert == "GIA"))
m2 <- update(m1, ~ . + carat)
m3 <- update(m2, ~ . + cut)
m4 <- update(m3, ~ . + color)
m5 <- update(m4, ~ . + clarity)
mtable(m1, m2, m3, m4, m5)##
## Calls:
## m1: lm(formula = logprice ~ I(carat^(1/3)), data = subset(diamondsbig,
## price < 10000 & cert == "GIA"))
## m2: lm(formula = logprice ~ I(carat^(1/3)) + carat, data = subset(diamondsbig,
## price < 10000 & cert == "GIA"))
## m3: lm(formula = logprice ~ I(carat^(1/3)) + carat + cut, data = subset(diamondsbig,
## price < 10000 & cert == "GIA"))
## m4: lm(formula = logprice ~ I(carat^(1/3)) + carat + cut + color,
## data = subset(diamondsbig, price < 10000 & cert == "GIA"))
## m5: lm(formula = logprice ~ I(carat^(1/3)) + carat + cut + color +
## clarity, data = subset(diamondsbig, price < 10000 & cert ==
## "GIA"))
##
## =========================================================================
## m1 m2 m3 m4 m5
## -------------------------------------------------------------------------
## (Intercept) 2.671*** 1.333*** 0.949*** 1.341*** 0.665***
## (0.003) (0.012) (0.012) (0.010) (0.007)
## I(carat^(1/3)) 5.839*** 8.243*** 8.633*** 8.110*** 8.320***
## (0.004) (0.022) (0.021) (0.017) (0.012)
## carat -1.061*** -1.223*** -0.782*** -0.763***
## (0.009) (0.009) (0.007) (0.005)
## cut: Ideal 0.211*** 0.181*** 0.131***
## (0.002) (0.001) (0.001)
## cut: V.Good 0.120*** 0.090*** 0.071***
## (0.002) (0.001) (0.001)
## color: E/D -0.083*** -0.071***
## (0.001) (0.001)
## color: F/D -0.125*** -0.105***
## (0.001) (0.001)
## color: G/D -0.178*** -0.162***
## (0.001) (0.001)
## color: H/D -0.243*** -0.225***
## (0.002) (0.001)
## color: I/D -0.361*** -0.358***
## (0.002) (0.001)
## color: J/D -0.500*** -0.509***
## (0.002) (0.001)
## color: K/D -0.689*** -0.710***
## (0.002) (0.002)
## color: L/D -0.812*** -0.827***
## (0.003) (0.002)
## clarity: I2 -0.301***
## (0.006)
## clarity: IF 0.751***
## (0.002)
## clarity: SI1 0.426***
## (0.002)
## clarity: SI2 0.306***
## (0.002)
## clarity: VS1 0.590***
## (0.002)
## clarity: VS2 0.534***
## (0.002)
## clarity: VVS1 0.693***
## (0.002)
## clarity: VVS2 0.633***
## (0.002)
## -------------------------------------------------------------------------
## R-squared 0.9 0.9 0.9 0.9 1.0
## adj. R-squared 0.9 0.9 0.9 0.9 1.0
## sigma 0.3 0.3 0.3 0.2 0.2
## F 2700903.7 1406538.3 754405.4 423311.5 521161.4
## p 0.0 0.0 0.0 0.0 0.0
## Log-likelihood -60137.8 -53996.3 -43339.8 37830.4 154124.3
## Deviance 28298.7 27291.5 25628.3 15874.9 7992.7
## AIC 120281.6 108000.5 86691.6 -75632.8 -308204.5
## BIC 120313.8 108043.5 86756.0 -75482.6 -307968.4
## N 338946 338946 338946 338946 338946
## =========================================================================Predictions
Example Diamond from BlueNile: Round 1.00 Very Good I VS1 $5,601
#Be sure you’ve loaded the library memisc and have m5 saved as an object in your workspace.
thisDiamond = data.frame(carat = 1.00, cut = "V.Good",
color = "I", clarity="VS1")
modelEstimate = predict(m5, newdata = thisDiamond,
interval="prediction", level = .95)
exp(modelEstimate)## fit lwr upr
## 1 5040.436 3730.34 6810.638Evaluate how well the model predicts the BlueNile diamond’s price. Think about the fitted point estimate as well as the 95% CI.
Final Thoughts
Notes:
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